The errant Snark was aimed at Ascension Island, but landed in Brazil. I think the problem was something besides not being able to see the stars.
According to a source I found on the web (an always accurate and relivant source) above 45,000 feet cloud cover should not interfer with astronavigation systems. This would mean that the Snark would have to fly near its maximum altitude most of the flight.
The max height of cloud cover varies with the height of the tropopause. Generally speaking, outside of the tropics, the tropopause is below 45kft. This does depend on weather, and the tropopause could reach 30kft or lower during the winter in the arctic. With thunderstorms, you can have clouds above the tropopause, but this is a relatively rare occurance, and with proper weather forecasting, should pose relatively little problem.